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uncle_w

20th May 2017, 19:42
Not a great enthusiast of numericals but always ready to have a go.
Unfortunately have failed to see a way into this one. A hint to start to me off would be appreciated. Thanks folk.
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unclued

20th May 2017, 20:51
Uncle, I started with 6dn. The coded code number would most likely leave a 1 in the top right corner of the code square. This cuts down the possible squares.

I fear I must start again because I have got everything to fit EXCEPT I have the sum of 20 digits as 96 but 1 across codes to 94. It's so annoying. Can anyone confirm whether I need to begin again? Thanks.
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durban

20th May 2017, 21:58
I started with the combination of 2 ac and 3 dn, together with 7 ac needing to be a divisor, as in its clue, AND needing its digits to sum to at least 12, because of 2 dn and the description of 2-digit answers in the preamble. But not yet finished, so can't help unclued.
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wintonian

20th May 2017, 22:22
Unclued, I think you must have gone wrong somewhere, because the sum of the 20 digits in the grid is 98.

With having to encode the four 2-digit answers, this puzzle involved me in a lot of brute computation where I tried all possible combinations in some places. You are correct that looking at 9ac and 6dn is a good starting point. As the code number has only two digits, the third digit in the top row of the code-square must be 1, 2 or 3. However, if you encode the code number, which is the first and second digits in the code-square, then this is encoded as the second and third digits. Hence the bottom right hand cell in the grid must be 1, 2 or 3. But as 6dn is a square, it can’t end in 2 or 3, so it must end in 1.

There are only five three-digit squares ending in 1, and all of them have an even number as their middle digit. Because the middle digit of 6dn is the last digit of 7ac, this means that 7ac is even, and as 3dn is a multiple of 7ac, 3dn is also even. Looking at the intersection of 2ac and 3dn and noting that 3dn is the reverse of 2ac leaves only a restricted choice of numbers for 2ac (particularly as 2ac is a multiple of another grid entry and so cannot be prime).

There is a very restricted number of combinations for 2ac, 3dn, 7ac and 6dn that satisfy all the requirements, and there are therefore very few possible answers for 2dn before this is encoded. I tried all possible Playfair code-squares (there are 56 of them, as the first digit can in theory be any of the eight digits from 2 to 9 (zero is specifically excluded and 1 can’t be in the code number because it’s already accounted for as the third digit in the top row of the code-square), and the second digit has to be a different digit, so there are 8 x 7 = 56 possibilities. Although I was able quite quickly to reduce the possible code numbers to only two of these 56 possibilities, I didn’t confirm the actual code number until right at the end, solving 1ac and 1dn together. Another route might have got there more quickly, however.
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unclued

21st May 2017, 07:15
Thanks Wintonian. I followed exactly the same path as you but must have made a mistake with 2 / 3 / 7. Frustrating to get everything else to fit except the very last stage!
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dryden

21st May 2017, 09:08
Having just finished after hours of blood, sweat and tears, I thought I'd check to see if anyone had found a quicker route than I did. So far it appears not. Wintonian's path is the precise one I followed, but it involved an awful lot of experimenting with trial grids even after narrowing down the possibilities for 7a.

I much prefer numerical puzzles where it's possible to trace a logical route from beginning to end with the minimum of trial and error.
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gitto

21st May 2017, 10:42
I seem to have solved this using only 2a,7a,3d,5d and 7d + some (possibly fortuitous) logic. Once you have deduced the top right number in the code square, I found most of the possible permutations disappeared, leaving me with only two choices for 2a,3d and 7a. That gave 2 choices for 2d, which in turn led to a small number of permutations for the code square.
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xij

21st May 2017, 17:12
Solving 7a is the critical factor. I spent hours going through all the permutations, finding only two and, unfortunately, proceeding with the wrong one first. Once I got the correct one it was fairly plain sailing. Only held up by forgetting to encode 1a.
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theambler

21st May 2017, 19:45
Hi Just starting to tackle this one but PUZZLED!!!
When the notes talk of " all 2digit clue answers" does that mean that some clue answers are three digit??? Certainly some grid entries are 3 digit. How do you encrypt 2digs into 3digs.

Can you see my problem Hope you can help
Kind Regards Thea(o)
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bunty

21st May 2017, 19:51
the 3 digit answers are normal .....just enter them in the grid....the 2 digit answers have to be encoded using the playfair code ...which you have to discover
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